Showing papers in "Transportation Research Record in 1986"

Modeling the relationship of accidents to miles traveled

Abstract: Consideration of highway safety studies in a time-space domain is used to introduce the concept that different study designs result in different underlying probability distributions describing accident occurrence Poisson regression is proposed as a superior alternative to conventional linear regression for many safety studies because it requires smaller sample sizes and has other desirable statistical properties Models are estimated using accident, travel mileage, and environmental data from the Indiana Toll Road A pooled model including all accidents revealed that accident occurrence increases with automobile vehicle miles of travel (VMT), truck VMT, and hours of snowfall Segmentation of the data into subsets that describe different types of collisions revealed that automobile accidents are much more sensitive to environmental conditions than are truck accidents Use of the segmentation technique allowed a much clearer understanding of the effects of travel mileage on accident occurrence than could have been obtained from the pooled data alone

Quantitative functional group analysis of asphalts using differential infrared spectrometry and selective chemical reactions--theory and application

Abstract: An analytical method is described for the rapid quantitative analysis of seven highly polar chemical functional groups present in asphalt or formed in asphalt during oxidative aging. The method employs infrared spectrometry combined with the specialized use of selective chemical reactions and differential spectra for quantification of the analytical absorption bands of interest. The naturally occurring functional groups determined are carboxylic acids and their salts, 2-quinolone types, phenolics, and pyrrolics; those formed on oxidation are ketones, anhydrides, small amounts of acids, and sulfoxides. Several selected applications of the functional group analysis as applicable to composition-related problems in asphalt technology are presented.

Passenger car equivalents for trucks on level freeway segments

Abstract: The term passenger car equivalent (PCE) was introduced in the 1965 Highway Capacity Manual. Since 1965, considerable research effort has been directed toward the estimation of PCE values for various roadway types. However, at present, there is neither a commonly accepted nor clearly defined theoreical basis for the concept of passenger car equivalency. Two components of a theoretical basis for equivalency are defined in this paper: (a) that the basis for equivalence should be the parameters used to define level of service for the roadway type in question, and (b) that the PCE formulation should be expressed in terms of variables that reflect the relative importance of three factors that contribute to the overall effect of trucks on the roadway type. The three factors are: (a) trucks are larger than passenger cars, (b) trucks have operating capabilities that are inferior to those of passenger cars, and (c) trucks have a physical impact on nearby vehicles and a psychological impact on the drivers of those vehicles. The two components of the theoretical basis were used to evaluate the merits of three approaches to estimating PCEs for level freeway segments: (a) the constant volume-to-capaciy ratio approach, (b) the equal-density approach, and (c) the spatial headway approach. It was concluded that the spatial headway approach was appropriate for level, basic freeway segments, and a PCE formulation expressed in terms of headway measurements was derived.

International roughness index: relationship to other measures of roughness and riding quality

Abstract: Different measures of road roughness with varying degrees of reproducibility and repeatability have been applied by various agencies in the world, but the exchange of roughness information has been hampered by a lack of an acceptable reference and a quantitative basis for relating the different measures. Presented in this paper is such a basis developed from an analysis of data from the International Road Roughness Experiment (IRRE) and other sources. The International Roughness Index (IRI), developed from the IRRE as a suitable calibration standard for all response-type and profilometric instruments, is the transferable reference scale. It is the metric equivalent of a reference inches/mile index. Two-way conversion relationships and confidence intervals are presented for the Quarter-car Index (QI), British Bump Integrator trailer index (BI), and various profile numerics of the French Analyseur de Profil en Long (APL) (longitudinal profile analyzer) profilometer from the IRRE, and for the Serviceability Index from other sources. The characteristics of each scale, and the sources of variation and range of application of the conversions are discussed.

Use of surface waves in pavement evaluation.

Abstract: Material characterization of pavement systems in situ is required for determining load capacity and assessing the performance and possible need for rehabilitation or replacement of the system. Nondestructive tests are usually carried out for this purpose. Desirable features of nondestructive tests are speed of operation, economy, and a sound theoretical basis compatible with the in situ data collection procedure. The most popular methods in this category are the falling weight deflectometer (FWD) and the Dynaflect. These methods are fast for in situ data collection; however, a rigorous data-reduction algorithm that can result in a unique solution and take into account the effect of the dynamic nature of the load has only begun to be developed. An alternative method of nondestructive testing has been under continuous development at the University of Texas. This method is called the spectral-analysis-of-surface-waves (SASW) method and is based on the theory of stress waves propagating in elastic media. The SASW method can be utilized to determine Young's modulus profiles of the pavement structure and underlying soil as well as the thickness of each layer. In this paper the theoretical aspects of the SASW method are discussed in detail. The experimental procedure is included only briefly because it has been presented comprehensively in earlier papers. Several case studies on different types of pavements with various thicknesses are presented to demonstrate the utility and versatility of the SASW method. In each case, the results are compared with those of the well-established crosshole seismic test that was performed at the same locations. The Young's modulus profiles from these two independent methods compare closely.

Implementation of work-zone speed control measures

Abstract: Recommendations for implementing speed control at construction and maintenance work zones are presented. The following implementation steps are identified and discussed: (a) determining the need for speed reduction, (b) selecting a reasonable speed, (c) selecting a speed control treatment based on effectiveness, practicality and cost, and (d) selecting a location for the speed control treatment implementation. Four speed control approaches are studied: flagging, law enforcement, changeable message signs, and effective lane width reduction. The advantages and disadvantages of each of these approaches are discussed. Limited cost data for each of the approaches are also presented. The conclusions and recommendations are based on the results of field studies and observations at numerous street and highway work zones in Texas.

Evaluation of steel bridges using in-service testing

Abstract: Highway bridges often exhibit higher strengths than indicated by AASHTO rating procedures. This is because the code is inherently conservative and is intended to be applied to general situations. A more appropriate approach is to incorporate field observations in the rating process. A field measurements (weigh-in-motion) system is capable of providing all pertinent data on the loading and response of highway bridges. The data collected include measured stresses and girder distribution factors in addition to truck weights and volumes. The data are then incorporated in a working stress design rating or in a reliability-based safety evaluation of bridge members. Results from an example site indicate high safety levels despite the large numbers of permit vehicles allowed.

The international road roughness experiment: a basis for establishing a standard scale for road roughness measurements

Abstract: With the general lack of equivalence between the many methods and measures by which road roughness is characterized, standardized indices offer the means to achieve a time-stable data base that can be utilized by all. The International Road Roughness Experient (IRRE) was organized in Brasilia, Brazil, to find a suitable index and to quantify the relationships between different equipment and roughness indices in use. Roughness measurements were made on 49 test sites by diverse types of equipment in common use. The data were analyzed to determine the equivalence between the roughness measures that could be obtained with each type of equipment and whether one common measure was applicable to all. The results from the IRRE showed that a standard roughness index is practical and measurable by most of the equipment in use today, whether of the profilometer or road meter type. As a result of the IRRE, a standard index was selected that is based on the quarter-car analysis method with standard parameter values and a reference speed of 80 km/h. Provided in this paper is the background on the fundamental of roughness characterization that guided the selection of the standard road roughness index.

Asphalt composition tests: their application and relation to field performance

Abstract: The application of chemical analysis to specific questions about asphalt and other tests to determine asphalt quality are discussed. Asphalt chemistry is complex; even with the analytical tools available, it would be almost impossible to identify and quantify all the components of even a single asphalt. Asphalt has commonly been analyzed by separating it into fractions on the basis of solubility, absorption, or molecular size. The fractions obtained are operationally or procedurally defined. The chemistry of the fractions has been only broadly defined. These fractional separation tests may be useful in fingerprinting an asphalt or in following changes that may occur during the manufacture, hot-mix processing, or in-use life cycle of a single asphalt. They do not, however, unravel the chemical composition of asphalt. Compositional tests based on fractional separation have not correlated reliably with field performance, nor have ratios based on the fractions. Physical and rheological tests have been shown to correlate with road performance on numerous test roads. These performance-related tests remain the most reliable guide to asphalt quality. Construction practices play a significant role in asphalt durability. High air void content has been shown to override any differences between asphalts. Asphalts from many sources perform well in roads. With this in mind, it appears unlikely that functional specifications based on composition could be devised. The performance-related thin film ovens and viscometers, and possibly new performance-related physical tests, will continue to provide a reasonable way of describing asphalt quality without directly confronting the almost impossible task of describing a most complex chemical material.

Methodology for planning and operations management of airport terminal facilities

Abstract: An approach to the systematic evaluation of the performance of airport terminal facilities is presented in this paper. The proposed methodology adopts new concepts to establish service standards through special surveys that can achieve better interpretation of capacity of individual facilities by relating demand levels imposed to relevant service measures. It can enhance existing practices in planning and management of airport terminals, and may prove to be a practical and convenient tool to airport terminal planners, consultants, and airport managers. The methodology is intended to be simple in structure, and moderately easy to implement. It is structured to minimize data requirements and uses simple measures and practical techniques that require minimal interference with terminal operations. Theoretical and practical aspects that feature the methodology and were considered in establishing its procedures are described and discussed.

Road classification according to driver population

Abstract: A proposed model for classification of rural roads according to driver population characteristics is described The driver population is distinguished by such traffic stream characteristics as trip purpose and trip length distribution, and the basic assumption made in the analysis is that the different traffic flow patterns observed at road sites result from different mixes of these characteristics The highway systems of the provinces of Alberta and Saskatchewan are investigated for the purpose of developing and testing the model The model suggests the application of some standard computational and statistical techniques to develop master patterns of traffic flow in order to recognize the driver population of a given road site The proposed model is simple to apply and its data requirements can easily be satisfied by the types of data collection programs normally undertaken by highway agencies Also, it is believed to be more objective and comprehensive than the existing methods used for the same purposes The road classification resulting from the model could be used as an important criterion for many highway planning and design functions Some examples of its application are (a) rationalization of provincewide traffic-counting programs, (b) design hourly volume considerations; (c) highway improvement programming; and, (d) highway capacity analysis

Dynamic analysis of falling weight deflectometer data

Abstract: The response of pavement systems to falling weight deflectometer (FWD) blows is evaluated by using a multidegree of freedom elastodynamic analysis. This analysis is based on a Fourier synthesis of a solution for periodic loading of elastic or viscoelastic horizontally layered strata. The method is verified for selected flexible pavement sections for which high-quality field and laboratory data are available in the literature. FWD deflection measurements at various geophone locations are compared by using dynamic as well as static analyses. The results indicate that inertial effects are important in the prediction of the pavement response. Conventional static analyses yield significantly different results and therefore yield erroneous (unconservative) predictions of pavement moduli back-calculated from deflection data. Elastodynamic analyses, based on fundamental material parameters (Young's modulus, mass density), appear to provide a useful vehicle for correlating pavement response between different loading modes (impulse, vibratory, etc.). Because resonance is a less important factor in the displacement response characteristics of pavements subjected to transient loading, deflection data obtained from transient loading devices are, in general, easier to interpret.

Relationships between composition, structure, and properties of road asphalts: state of research at the french public works central laboratory

Abstract: Reviewed is the past and ongoing research conducted at France's Laboratoire Central des Ponts et Chaussees (LCPC) (Public Works Central Laboratory) in the area of asphalt cements. The investigations cover the development of methods for characterizing the physicochemical and rheological properties of such materials, and the establishment of relationships between their composition, colloidal structure, and practical properties. For physicochemical characterization, the research makes use of such techniques as high-pressure liquid chromatography, gel permeation chromatography (GPC), and differential scanning calorimetry. The rheological behavior of materials is studied by the peeling technique, viscoelastisimetry, and viscosimetry on thin films (with specially designed apparatus). Theoretical studies have led to the proposal of a new rheological behavior model better suited to experimental results than conventional models, characterized by its analogy with the laws of chemical kinetics, and allowing the calculation of a structural parameter as well as a parameter dependent on energy per unit volume dissipated and having activation energy characteristics. The foregoing assessment brings out the effectiveness of the facilities set up by the LCPC, and it is important to note that the new characterization methods indicate that asphalt cements with the same specifications have substantially different physicochemical compositions and rheological behaviors. Among the most important results, it is demonstrated that GPC makes it possible to characterize the equilibrium of the colloidal structure of asphalt cement and to obtain information on the ability of asphaltenes to interact to form a more or less developed network responsible for the gel character of the rheological behavior noted. It is also demonstrated that information obtained by GPC on the interaction of asphaltene micelles is closely correlated with certain observed characteristics of rheological behavior.

Base course contamination limits

Abstract: Geotextiles have been used in pavement structures for two primary purposes: subgrade reinforcement and separation. Research to date has been concentrated on developing design procedures for incorporating geotextiles for subgrade reinforcement in areas with low-strength soils (CBR less than 3). In this paper the use of geotextiles as a separation mechanism in roadways with higher strength soils (CBR greater than 3) is evaluated. The primary effect of geotextiles in this application is to reduce the amount of contamination within the aggregate base layer. Contamination of this layer occurs primarily through intrusion of subgrade materials into the aggregate base. This intrusion changes the gradation of the base and results in reduced strength or stiffness as well as lower permeability. Geotextiles reduce the contamination in the aggregate base by modifying the process of subgrade intrusion, the level of stress at the subgrade interface, and the process of filtration. A laboratory study was conducted to illustrate the influence of added fines on the modulus of an aggregate base. The aggregate tested was a 1-in.-minus crushed aggregate with 5.5 percent passing the No. 200 (0.075-mm) sieve. The study showed that, for the materials tested, up to 6 percent added fines can be tolerated without adversely affecting the stiffness of the base. For U.S. Forest Service base courses, separation geotextiles need to limit subgrade intrusion to 2.5 percent if the initial aggregate has 5.5 percent fines, since the upper limit for proper drainage is 8 percent fines. Primary benefits from geotextiles include increased life of the pavement structure or reduced initial and long-term capital outlays, or both.

Rumble strips and paint stripes at a rural intersection

Abstract: A common cause of traffic accidents at low-volume rural intersections is failure by drivers on the minor approaches to stop or slow down sufficiently, as warranted. The current experimental field study compared the effectiveness of transverse paint stripes, such as those developed by the U.K. Transport and Road Research Laboratory, and similarly placed rumble strips in inducing drivers to reduce speed and stop at intersections. The experiment was conducted on the two minor approaches to the same four-way rural low-volume intersection. A geometrically converging pattern of 38 paint stripes, each 60 cm (2 ft) wide, were laid out over a distance of 270 m (886 ft) of one leg, and a similar pattern of rumble strips, 12 to 15 mm (1/2 to 5/8 in.) high, was laid on the opposite leg. A before-and-after and a crossover (after a year) experimental design were used. Speeds were monitored at eight points on each leg along 420 m leading to the intersection for a total of over 2,500 lead vehicles. The main results and conclusions are as follows: (a) paint stripes have only minor influence on driver behavior; (b) rumble strips lowered speeds by an average of 40 percent; (c) both treatments had a small positive effect on compliance rate; (d) with no pavement treatment, deceleration began at 150 m (492 ft) and peaked within the last 60 m (197 ft); (e) with rumble strips, most of the deceleration took place before the vehicle passed the first strip, followed by an additional deceleration within the last 60 m (197 ft); (f) rumble-strip effects remained stable after a year; and (g) a 150-m (492-ft) treatment of 12-mm strips is long enough to produce the positive effects of rumble strips.

Driver age and highway safety

Abstract: A data base of more than 50,000 police-reported accidents on Michigan Interstate and trunkline highways in 1982 and an accident surrogate exposure method were used in an investigation of the relationship among driver characteristics, vehicle size, and relative accident involvement. The relationship between driver age and accident involvement was strong regardless of the vehicle weight category, with younger and older drivers involved more often. The relationship is strong for urban areas, but a strong trend is not evident in a rural driving environment. Different accident types revealed slightly different U-shaped curves, possibly demonstrating a sensitivity of driver age to the urban driving task.

Benefits and safety impact of night work-zone activities

Abstract: A literature review and discussions with highway and transportation officials in several states provided information on issues relating to the planning, safety, and traffic control aspects of night maintenance and construction activities, and their advantages and disadvantages. The information was used to develop general guidelines for nighttime maintenance and construction work. Although there are many potential disadvantages to working at night, it is believed that experience, proper planning, and attention to workmen and motorist safety make the night alternative feasible for selected work.

Availability of information and dynamics of departure time choice: experimental investigation (discussion)

Abstract: The effect of information availability on the dynamics of user behavior in urban commuting systems is investigated through an experimental procedure that involves real commuters interacting in a simulated traffic system under two distinct informational situations: in one only the decision maker's own performance on the previous day is available, and in the other complete information about the system's performance on the previous day is available The results are examined from the perspective of a theoretical framework articulated previously in conjunction with the results of the first, limited-information, experiment The focus of this paper is on the results of the complete-information experiment relative to those obtained in the first one It is found that additional information raises users' aspiration levels and generally improves their predictive capability, but results in greater day-to-day departure time switching and longer convergence periods to a steady state, which is superior, in terms of user costs, to that attained under limited information

Asphalt aggregate mixtures

Abstract: In France, mechanical tests are used essentially for characterizing the performance of bituminous concretes for mix design purposes, production control requiring retroaction times that are much too short. Compacting characteristics are studied with an imposed angle gyratory shear compacting press; an indication of the results obtained on the job site is obtained by correlation with a pilot compactor. A number of plate samples are prepared with a laboratory-tired compactor. Resources of increasing complexity are used for the study of permanent deformation characteristics. The repeated compression test with a lateral load is used for research purposes, and the wheel-tracking rutting test is used for mix design studies. Because the concern here was fatigue performance, the bending test was used to study the influence of composition factors. More recently, a shear fatigue test, which is more representative of the loads to which the thin surface courses are subjected, has been employed. However, fatigue tests are too costly and time consuming to be used for mix design studies, so a new test has been developed to measure stiffness moduli and to estimate fatigue properties. Secant moduli at different temperatures, linearity loss, and strength at 0 deg C is obtained by two regressions. For the mix design, the diversity of functions to be provided and the cost of testing make it necessary to rank the problems according to importance and to define a methodology that can be adapted to different cases.

Field validation of intersection capacity factors

Abstract: Presented are the results of a series of saturation flow surveys conducted throughout the United States at signalized intersections. The purpose of this research was to verify the saturation flow rates and traffic volume adjustment factors used in various capacity analysis procedures by collecting a relatively extensive data base. Saturation flow headways for more than 20,000 observations were collected for a series of 12 geometric, traffic characteristic, and environmental factors and compared with baseline saturation flow headways for various signal cycle length and phase combinations. Vehicle blockage and lane distribution surveys were conducted for 19,000 additional observations. Based on the results of these surveys, a series of modified adjustment factors is suggested to allow the analyst to determine modified saturation flow rates when calculating signalized capacity.

Factors that determine mode choice in the transportation of general freight

Abstract: This study examines the factors that influence the mode choice decisions of shippers of general freight commodities in the Atlantic provinces of Canada. The study employed a mail-response questionnaire directed to randomly selected manufacturers to determine the basis of each firm's decision to ship by its regular mode. Respondents were required to identify the product shipped most frequently by the firm and the most regular origin-destination link. They were then required to provide pertinent details, such as transit time, shipping costs, and frequency of shipments, relating to the shipment of that product on the identified origin-destination link. Linear logit models were used to determine the variables that influence the selection of various modes for goods shipments and the relationship between the utility of each mode and the explanatory variables. The models obtained were as intuitively expected. It is concluded that logit analysis using survey data represents a valid and potentially more useful methodology than the use of waybill data. It is recommended that further research using the suggested model forms and data obtained from personal interviews of shippers would improve the quality of the results and provide a greater understanding of the shipper mode choice decision process.

Climatic-materials-structural pavement analysis program

Abstract: The Climatic-Materials-Structural (CMS) program has been set up to introduce climatic effects into the analysis of multilayered flexible pavement systems. The program may be used with selected pavement structural and performance models to analyze a pavement system. It can also be employed as a tool to analyze existing pavement systems in order to obtain estimates of future maintenance requirements. The CMS program is compatible with several pavement structural models for determining radial stresses, strains, and displacements. These structural models include the ILLI-PAVE model, ILLI-PAVE algorithms, and elastic layer analysis. The accuracy of the CMS output depends mainly on the quality of the inputs. It is important that boundary conditions, climatic conditions, and material properties properly represent the system to be analyzed. With representative inputs the CMS program will give realistic values for temperature and moisture profiles and material strength properties. Although future research is required to validate the overall model, the validity of the individual parts of the CMS program has been shown. Analysis of existing pavement systems and comparison of CMS outputs with actual field conditions are recommended. It is expected that further validation studies will confirm the belief that the CMS program provides an economical and realistic means of analyzing multilayered flexible pavement systems by accounting for climatic effects on pavement materials.

Entering headway at signalized intersections in a small metropolitan area

Abstract: The entering headway is a parameter of fundamental importance to traffic engineers. It has major applications in intersection capacity and signal timing. However, the attention given to this matter appears to be inadequate. It was indicated by a literature review that past efforts tended to be infrequent, fragmented, and limited in scope. No studies were found using data from small cities or investigating factors that affect entering headways. This study, aimed at measuring entering headways in a small city and examining six factors, was conducted on sites in Lawrence, Kansas. Entering headway values from a total of 1,899 traffic queues were recorded by using video camera equipment. From the data, mean entry headways of vehicles 1 through 12 were found to be 3.80, 2.56, 2.35, 2.22, 2.16, 2.03, 1.97, 1.94, 1.94, 1.78, 1.64 and 1.76. Of the six factors studied, the following were also found: the signal type and the time of day have little influence on vehicular entering headways; vehicles in the inside lane of an intersection approach have lower entering headways than vehicles in the outside lane; vehicles in an intersection approach with lower speed limits have higher entering headways; vehicles in intersection approaches of streets with lower functional classifications have higher entering headways; and longer queue lengths appear to produce shorter entering headways for vehicles. However, because of data limitations, findings on the factors studied shall be viewed as only preliminary.

Constraints on individual travel behavior in a brazilian city

Abstract: In this paper the statistical and predictive performance of two disaggregate choice models that incorporate probabilistic choice set formation are compared with a standard logit specification. The empirical work is conducted with work mode choice data from a Brazilian city. For the type of travel demand analyzed it is found that, although statistically inferior to the probabilistic choice set specifications, the standard logit specification, allied with market segmentation, is a robust formulation in both statistical and predictive terms. Recommendations for future research work in probabilistic choice set modeling are presented.

Geotechnical error analysis

Abstract: A simple method is presented for rationalizing the treatment of uncertainties in geotechnical engineering calculations. This method uses a reliability index to express the degree of confidence in a calculation. The reliability index combines the best estimate with a standard deviation reflecting four principal sources of uncertainty, spatial variability, measurement noise, model bias, and limited data. An example involving shallow footing design is used for illustration.

On predicting pavement surface distress with empirical models of failure times

Abstract: A statistical procedure that overcomes common difficulties in the development of distress models from empirical data is described and applied in an example. The method applies failure-time theory, using maximum likelihood methods so that censored data can be included to prevent statistical bias in the predictions. The variability of failure times is represented by a Weibull distribution because that is considered the most appropriate for the concurrent mechanisms of fatigue and weathering and is flexible in shape. An example application of the procedure to a major analysis of Brazilian condition data shows that it permitted the use of a much wider data base than would otherwise be possible and produced important results that quantify strong effects of weathering and variability.

Further studies on lateral load distribution using a finite element method

Abstract: A computer program, SALOD, has been written for the Florida Department of Transportation to evaluate the lateral load distribution characteristics of simple-span bridges in flexure. Bridges may be prestressed concrete girder, steel girder, T-beam, or flat slab. The program uses moment influence services generated by the STRUDL finite element system for representative simple-span bridges determined by a statewide survey. Up to three vehicles are placed in critical locations to determine the maximum distribution factors. The effect of span length, which is neglected in AASHTO, was found to be considerable. AASHTO results were found to be slightly unconservative for short spans and quite conservative for longer spans. Field testing, reported elsewhere, has been completed on eight bridges. Comparisons of results from finite element models and measurements of applied truck loading have been generally good. Comparisons of flexural distribution factors from SALOD and the Ontario Highway Bridge Design Code (OHBDC) for prestressed girder bridges showed generally good agreement. However, OHBDC indicates more sensitivity to girder spacing than does SALOD. AASHTO simple-span results compare quite well with SALOD for exterior girders. A limited study of shear distribution factors for girder-slab bridges showed that shear distribution factors do not vary significantly with span length and that AASHTO factors appeared adequate for design.

The safety effect of conversion to all-way stop control

Abstract: Past studies documenting the safety effect of converting intersection traffic control to all-way stops have consistently shown impressive accident reductions. Because, ordinarily, it was high-accident locations that were converted, it was difficult to know how much of the reduction was real and how much was an artifact of regression-to-the-mean. Data from three recent studies were reanalyzed and debiased. In addition, a new data set was assembled and examined. Analysis revealed that, although somewhat inflated, the reductions reported in the earlier studies were quite real and were confirmed by the new data. The empirical information contained in the data sets was captured in likelihood functions and the four functions were joined. Taken individually, the four data sets showed reductions in total accidents ranging from 37 to 62 percent. The joint likelihood function indicates a most likely accident reduction of 47 percent in total accidents.